Flow-sensitive type systems and the ambient calculus

The Ambient Calculus was developed by Cardelli and Gordon as a formal framework to study issues of mobility and migrant code. Numerous analyses have been developed for numerous variants of that calculus. We take up the challenge of developing, in a type-based setting, a relatively precise “topology” analysis for the original version of the calculus. To compensate for the lack of “co-capabilities” (an otherwise increasingly popular extension), the analysis is flow-sensitive, with the actions of processes being summarized by “behaviors”. A subject reduction property guarantees that for a well-typed process, the location of any ambient is included in what is predicted by its type; additionally it ensures that communicating subprocesses agree on their “topic of conversation”. Based on techniques borrowed from finite automata theory, type checking of type-annotated processes is decidable (though potentially exponential).